derivative f(x)=(1-4x)/(1+4x)

Lösung

ableitung von

f (x) = \frac{1 - 4 x}{1 + 4 x}

- \frac{8}{( 1 + 4 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1 - 4 x}{1 + 4 x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 1 - 4 x ) ( 1 + 4 x ) - \frac{d}{d x} ( 1 + 4 x ) ( 1 - 4 x )}{( 1 + 4 x ) ^{2}}

\frac{d}{d x} (1 - 4 x) = - 4

\frac{d}{d x} (1 + 4 x) = 4

= \frac{( - 4 ) ( 1 + 4 x ) - 4 ( 1 - 4 x )}{( 1 + 4 x ) ^{2}}

Vereinfache

\frac{( - 4 ) ( 1 + 4 x ) - 4 ( 1 - 4 x )}{( 1 + 4 x ) ^{2}} : - \frac{8}{( 1 + 4 x ) ^{2}}

= - \frac{8}{( 1 + 4 x ) ^{2}}

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